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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Closures of conjugacy classes in classical real linear Lie groups. II


Author: Dragomir Ž. Djoković
Journal: Trans. Amer. Math. Soc. 270 (1982), 217-252
MSC: Primary 22E15
DOI: https://doi.org/10.1090/S0002-9947-1982-0642339-4
MathSciNet review: 642339
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Abstract: By a classical group we mean one of the groups $G{L_n}(R)$, $G{L_n}(C)$, $G{L_n}(H)$, $U(p, q)$, ${O_n}(C)$, $O(p, q)$, $S{O^{\ast }}(2n)$, $S{p_{2n}}(C)$, $S{p_{2n}}(R)$, or $Sp(p, q)$. Let $G$ be a classical group and $L$ its Lie algebra. For each $x \in L$ we determine the closure of the orbit $G \cdot x$ (for the adjoint action of $G$ on $L$). The problem is first reduced to the case when $x$ is nilpotent. By using the exponential map we also determine the closures of conjugacy classes of $G$.


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Keywords: Classical group, adjoint representation, orbit, conjugacy class, Young diagram
Article copyright: © Copyright 1982 American Mathematical Society